Global Attractors For Two Kinds Of Thermoelastic Coupled Beam Equations

The so-called thermoelastic equation is the short of elastic mechanics in physics,which is a mathematic model according to regular of distortion of the elastomer and the distribution of the temperature.At present,the thermoelastic coupled equations have been researched widely,which related to the natural science and has a practical background,In this paper,we mainly discussed the non-autonomous thermoelastic coupled beam system.It include of the initial boundary value problem of the global attractors for the thermoelastic beam equations with double memory and the global attractors for the thermoelastic beam equations with damping and memory.Firstly,we transform the nonautonomous system into the autonomous system.Proving the posedness theorem by the semigroup theory in the same time,Then we use the classical integral estimation method to prove the infinite dimensional dynamical system corresponding to the existence of a bounded absorbing set,Finally we prove of corre-sponding solution semigroups of asymptotically compact by using the standard method.So the existence of global attractor of operator semigroups is obtained in phase space.The full text structure is as follows:The first chapter briefly introduces the background and current situation of the re-search,at the same time,in which also introduce the main work and the main results in this paper.The second chapter introduces some basic knowledge used in this paper,including the basic space as well as their relationship,lemma,concept and hypothesis,as well as some commonly used inequality.The third chapter is devoted to the existence of solution and the existence of the global attractor.The fourth chapter is devoted to the existence of the global attractor for the Initial boundary value problem of coupled thermoelastic beam equation with strong damping and memory.